I would prefer to have our resident tax professional answer this, but until then, I'll offer my opinion. As usual, warning, I may be very wrong.
Income and benefits (vacation pay, etc.) earned from work performed in the US prior to arriving in the UK (for UK tax purposes) should not be taxable by HMRC no matter when the actual payment is made (even if after arriving in the UK for tax purposes). The caveat, for HMRC, is IF those funds earn income (interest, etc.) after one arrives in the UK and is taxed on the arising basis, and even if the funds remain in the US, that subsequent income (interest, etc.) is subject to taxation by HMRC.
Pension plan contributions and health insurance premiums that have been maintained and taxed in the US after one arrives in the UK (for tax purposes and arising basis) are of no concern to HMRC. HMRC will tax the individual on the gross income (prior to the deductions) in the UK and it is up to the individual to reclaim the offsetting tax credits via their US tax return for the applicable year.
If one has retained CSI in the US (and I have no idea what that is) to meet the ObamaCare mandate, then that is the individuals concern and of no interest to HMRC. Again, the full, gross amount of income is taxable by HMRC. The individual, resident in the UK, has the ability to avoid any ObamaCare mandate by filing IRS Form 8965. Not HMRC's problem.
If I read the Tax Cuts and Jobs Act correctly, the ObamaCare mandate will go away in 2019, so the need to file 8965 should disappear. Shame, it was by far the easiest form to complete.
We have BUPA coverage in the UK, related to past work prior to retirement. It is of no consideration on either our HMRC filings, or US filings. For the IRS/HMRC, it is the same as buying new socks. It's our choice of expenditure. If the BUPA were to be offered as a benefit to a UK employee of a UK company, the amount of the benefit would taxable as a "benefit in kind" by HMRC. A US return would tax the gross salary, including the benefit, and a tax credit would be used to offset US tax due via UK tax paid on the US return.
Again, I may be totally up the Swanee on this, especially since I don't know what CIS is.